Definition df-im 15045

Description: Define a function whose value is the imaginary part of a complex number. See imval 15051 for its value, imcli 15112 for its closure, and replim 15060 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.)

Assertion

Ref	Expression
df-im	⊢ ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))

Detailed syntax breakdown of Definition df-im

Step	Hyp	Ref	Expression
1		cim 15042	. 2 class ℑ
2		vx	. . 3 setvar 𝑥
3		cc 11105	. . 3 class ℂ
4	2	cv 1541	. . . . 5 class 𝑥
5		ci 11109	. . . . 5 class i
6		cdiv 11868	. . . . 5 class /
7	4, 5, 6	co 7406	. . . 4 class (𝑥 / i)
8		cre 15041	. . . 4 class ℜ
9	7, 8	cfv 6541	. . 3 class (ℜ‘(𝑥 / i))
10	2, 3, 9	cmpt 5231	. 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
11	1, 10	wceq 1542	1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))

This definition is referenced by:  imval  15051  imf  15057  cnre2csqima  32880